Laws of Motion with Static Equilibrium

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Homework Help Overview

The discussion revolves around a problem involving static equilibrium and the laws of motion, specifically focusing on determining the angles and tensions in a system with weights w1 and w2. The scenario assumes the system is at rest, with given values for the weights and an angle.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of trigonometric relationships to find tensions in the ropes and question the validity of their equations. There is an exploration of the vertical components of tension and how they relate to the weights.

Discussion Status

The discussion is ongoing, with participants attempting to clarify their understanding of the tension equations and the relationships between the forces. Some guidance is provided regarding the nature of tension in pulleys, but no consensus has been reached on the correct approach or values.

Contextual Notes

Participants are working with specific values for weights and angles, and there is mention of potential mistakes in calculations. The problem context suggests a need for careful consideration of the static equilibrium conditions.

Keithkent09
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Homework Statement


Find θ and W in the figure below where w1 = 16.0 N, w2 = 25.0 N, and α = 66.5°, assuming that the arrangement is at rest.

Homework Equations


T_1=25/sin(alpha)
F_x=-T_1cos(alpha)+T_2cos(theta)
F_y=T_1sin(alpha)+T_2sin(theta)-2

The Attempt at a Solution


I tried to use the above equations to solve for the three unknowns. First I found the tension of the string on the left, then plugged that into the second two equations to find the remaining values and I could not get the correct answers.
 

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Keithkent09 said:
T_1=25/sin(alpha)

Why is this true? What are tensions T1 and T2 in each rope?
 
Sorry I meant that it is 16/sin(alpha).
This is because the vertical component of T_1 is 16 because of w_1. So using trig T_1=17.447. I am doing this the correct way and just making some kind of simple mistake?
 
A pulley changes the direction of the tension without changing its magnitude. What is the tension in the piece of the leftmost rope that is hanging straight down?
 

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